Updated headers

Author: Chillee

content/geometry/SegmentIntersection.h

@@ -1,38 +1,45 @@
 /**
- * Author: Ulf Lundstrom
- * Date: 2009-03-21
+ * Author: Victor Lecomte, chilli
+ * Date: 2019-04-27
  * License: CC0
- * Source:
+ * Source: https://vlecomte.github.io/cp-geo.pdf
  * Description:\\
 \begin{minipage}{75mm}
-If a unique intersetion point between the line segments going from s1 to e1 and from s2 to e2 exists r1 is set to this point and 1 is returned.
-If no intersection point exists 0 is returned and if infinitely many exists 2 is returned and r1 and r2 are set to the two ends of the common line.
+If a unique intersetion point between the line segments going from s1 to e1 and from s2 to e2 exists then it is returned.
+If no intersection point exists an empty vector is returned. If infinitely many exist a vector with 2 elements is returned.
 The wrong position will be returned if P is Point<int> and the intersection point does not have integer coordinates.
 Products of three coordinates are used in intermediate steps so watch out for overflow if using int or long long.
-Use segmentIntersectionQ to get just a true/false answer.
 \end{minipage}
 \begin{minipage}{15mm}
 \includegraphics[width=\textwidth]{../content/geometry/SegmentIntersection}
 \end{minipage}
- * Status: Well tested with unitTest and with Kattis problem intersection.
+ * Status: Well tested with fuzz-test and with Kattis problem intersection.
  * Usage:
- * Point<double> intersection, dummy;
- * if (segmentIntersection(s1,e1,s2,e2,intersection,dummy)==1)
- *   cout << "segments intersect at " << intersection << endl;
+ * vector<P> inter = segInter(s1,e1,s2,e2);
+ * if (inter.size()==1)
+ *   cout << "segments intersect at " << inter[0] << endl;
  */
 #pragma once
 
 #include "Point.h"
 #include "onSegment.h"
-#include "SegmentIntersectionProper.h"
 
-template<class P> set<P> segInter(P a, P b, P c, P d) {
-    P out;
-    if (segInterProper(a, b, c, d, out)) return {out};
-    set<P> s;
-    if (onSegment(c, d, a)) s.insert(a);
-    if (onSegment(c, d, b)) s.insert(b);
-    if (onSegment(a, b, c)) s.insert(c);
-    if (onSegment(a, b, d)) s.insert(d);
-    return s;
+template <class P> bool segInterProper(P a, P b, P c, P d, P &out) {
+	double oa = c.cross(d, a), ob = c.cross(d, b),
+		   oc = a.cross(b, c), od = a.cross(b, d);
+	if (sgn(oa) * sgn(ob) < 0 && sgn(oc) * sgn(od) < 0) {
+		out = (a * ob - b * oa) / (ob - oa);
+		return true;
+	}
+	return false;
+}
+template<class P> vector<P> segInter(P a, P b, P c, P d) {
+	P out;
+	if (segInterProper(a, b, c, d, out)) return {out};
+	set<P> s;
+	if (onSegment(c, d, a)) s.insert(a);
+	if (onSegment(c, d, b)) s.insert(b);
+	if (onSegment(a, b, c)) s.insert(c);
+	if (onSegment(a, b, d)) s.insert(d);
+	return vector<P>(all(s));
 }

content/geometry/SegmentIntersectionProper.h

@@ -6,7 +6,6 @@ \section{Geometric primitives}
 	\kactlimport{SegmentDistance.h}
 	\columnbreak
 	\kactlimport{SegmentIntersection.h}
-	\kactlimport{SegmentIntersectionProper.h}
 	\columnbreak
 	\kactlimport{lineIntersection.h}
 	\kactlimport{sideOf.h}

content/geometry/chapter.tex

@@ -1,9 +1,9 @@
 /**
- * Author: Ulf Lundstrom
- * Date: 2009-04-09
+ * Author: Victor Lecomte, chilli
+ * Date: 2019-04-26
  * License: CC0
- * Source: Basic geometry
- * Description: Returns true iff p lies on the line segment from s to e. Intended for use with e.g. Point<long long> where overflow is an issue. Use (segDist(s,e,p)<=epsilon) instead when using Point<double>.
+ * Source: https://vlecomte.github.io/cp-geo.pdf
+ * Description: Returns true iff p lies on the line segment from s to e. Intended for use with e.g. Point<long long> where overflow is an issue.
  * Status:
  */
 #pragma once

content/geometry/onSegment.h

@@ -15,30 +15,30 @@ typedef vector<int> vi;
 namespace oldImpl {
 template<class P>
 int segmentIntersection(const P& s1, const P& e1,
-		const P& s2, const P& e2, P& r1, P& r2) {
-	if (e1==s1) {
-		if (e2==s2) {
-			if (e1==e2) { r1 = e1; return 1; } //all equal
-			else return 0; //different point segments
-		} else return segmentIntersection(s2,e2,s1,e1,r1,r2);//swap
-	}
-	//segment directions and separation
-	P v1 = e1-s1, v2 = e2-s2, d = s2-s1;
-	auto a = v1.cross(v2), a1 = v1.cross(d), a2 = v2.cross(d);
-	if (a == 0) { //if parallel
-		auto b1=s1.dot(v1), c1=e1.dot(v1),
-		     b2=s2.dot(v1), c2=e2.dot(v1);
-		if (a1 || a2 || max(b1,min(b2,c2))>min(c1,max(b2,c2)))
-			return 0;
-		r1 = min(b2,c2)<b1 ? s1 : (b2<c2 ? s2 : e2);
-		r2 = max(b2,c2)>c1 ? e1 : (b2>c2 ? s2 : e2);
-		return 2-(r1==r2);
-	}
-	if (a < 0) { a = -a; a1 = -a1; a2 = -a2; }
-	if (0<a1 || a<-a1 || 0<a2 || a<-a2)
-		return 0;
-	r1 = s1-v1*a2/a;
-	return 1;
+        const P& s2, const P& e2, P& r1, P& r2) {
+    if (e1==s1) {
+        if (e2==s2) {
+            if (e1==e2) { r1 = e1; return 1; } //all equal
+            else return 0; //different point segments
+        } else return segmentIntersection(s2,e2,s1,e1,r1,r2);//swap
+    }
+    //segment directions and separation
+    P v1 = e1-s1, v2 = e2-s2, d = s2-s1;
+    auto a = v1.cross(v2), a1 = v1.cross(d), a2 = v2.cross(d);
+    if (a == 0) { //if parallel
+        auto b1=s1.dot(v1), c1=e1.dot(v1),
+             b2=s2.dot(v1), c2=e2.dot(v1);
+        if (a1 || a2 || max(b1,min(b2,c2))>min(c1,max(b2,c2)))
+            return 0;
+        r1 = min(b2,c2)<b1 ? s1 : (b2<c2 ? s2 : e2);
+        r2 = max(b2,c2)>c1 ? e1 : (b2>c2 ? s2 : e2);
+        return 2-(r1==r2);
+    }
+    if (a < 0) { a = -a; a1 = -a1; a2 = -a2; }
+    if (0<a1 || a<-a1 || 0<a2 || a<-a2)
+        return 0;
+    r1 = s1-v1*a2/a;
+    return 1;
 }
 }
 typedef Point<double> P;
@@ -67,4 +67,5 @@ int main() {
             assert(eq(a[0], b[0]) && eq(a[1],b[1]));
         }
     }
+    cout<<"Tests passed!"<<endl;
 }